Asymptotic solution of the Boltzmann-Krook equation for the Rayleigh flow

An asymptotic solution of the Boltzmann-Krook equations for the Rayleigh shear flow is constructed. The flow consists of a reacting mixture of gases (0 and 02 molecules) and the chemical process is assumed to occur both in the flow and on the surface which is highly catalytic. The distribution functions, corresponding equations of motion and the boundary conditions on the averaged flow parameters are expanded in powers of the square root of the Knudsen number assumed to be small. The first order system is similar to the Navier-Stokes equations with no-slip boundary conditions. The second order system represents a slip flow with coefficients which depend on the solution of the first order system. One of ways to treat with the highly catalytic surface is also presented. The relationship among the diffusion velocity of atoms, the catalytic efficiency and the catalytic recombination rate constant on the surface are clarified and the effect of the catalytic efficiency on the heat transfer rate on the surface is discussed. Thesis Supervisor: Leon Trilling Title: Professor of the Department of Aeronautics and Astronautics, M.I.T. Acknowledgments I would like to thank Prof. Trilling for his valuable advice and comments during the course of bringing this work to completion.